Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of...
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Transcript of Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of...
![Page 1: Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of Physics, Inha University.](https://reader035.fdocuments.us/reader035/viewer/2022062806/56649f435503460f94c63f29/html5/thumbnails/1.jpg)
Inha Nuclear Physics Group
Relativistic Relativistic
Approach Approach
to QQ Potentialto QQ Potential2007. 12. 14
Jin-Hee Yoon
Dept. of Physics, Inha University
![Page 2: Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of Physics, Inha University.](https://reader035.fdocuments.us/reader035/viewer/2022062806/56649f435503460f94c63f29/html5/thumbnails/2.jpg)
Inha Nuclear Physics Group
Introduction
Relativistic Treatment of 2-Body Problem Composite systems with light quarks Systems with large coupling strengthDissociation and recombination of JJD + D+
Useful information on the suppression or the enhancement of in high-energy heavy-ion collisions
2-body Dirac equations of constraint dynamics- successfully tested on relativistic 2-body bound states in QE
D, QCD, & 2-body NN scattering. (Horace W. Crater et al., PRD74, 054028 (2006))
- Will be tested on heavy-quarkonium dissociation
![Page 3: Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of Physics, Inha University.](https://reader035.fdocuments.us/reader035/viewer/2022062806/56649f435503460f94c63f29/html5/thumbnails/3.jpg)
Inha Nuclear Physics Group
2-Body Constraint Dynamics
In a separable two-body basisParticles interacts pairwise through scalar and vector interactions.Spin-dependence is determined naturally.Yields simple Schrodinger-type equation.No cutoff parameter
![Page 4: Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of Physics, Inha University.](https://reader035.fdocuments.us/reader035/viewer/2022062806/56649f435503460f94c63f29/html5/thumbnails/4.jpg)
Inha Nuclear Physics Group
2-Body Constraint Dynamics
P. van Alstine et al., J. Math. Phys.23, 1997 (1982) Two free spinless particles with the mass-shell constraint
Introducing the Poincare invariant world scalar S(x,p1,p2)
Dynamic mass-shell constraint
Schrodinger-like equation
0 ,0 2
1
2
1
0
1
2
1
2
1
0
1 mpHmpH
),,(),,(
),,(),,(
2122122
2112111
ppxMppxSmm
ppxMppxSmm
),,( 212222 ppxVmpMpH iiiiii
w
mmm
w
mmw
mwb
wbVpw
HHH
ww
ww
2122
21
2
222
222211
and 2
with
)( where
0)(
![Page 5: Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of Physics, Inha University.](https://reader035.fdocuments.us/reader035/viewer/2022062806/56649f435503460f94c63f29/html5/thumbnails/5.jpg)
Inha Nuclear Physics Group
2-Body Constraint Dynamics
2-body Dirac Equation
where
)()( 22 wbVp w
TSSSSTSOSOSOSODw VVVVVVVVV 3210
)()12(cosh22sinh'2
'')12(cosh'2 222 rm
r
KF
r
KKFK
r
KFV D
22
0 22 AASSmV ww
r
KK
r
K
r
KF
r
FLV SO
2sinh')12(cosh)12(cosh'')(
2211
KqKlLV SO 2sinh'2cosh')( 212
KlKqLiV SO 2sinh'2cosh')( 213
r
KF
r
K
r
K
r
KKLrrV TSO
2sinh''2sinh)12(cosh')(ˆˆ
22121
r
K
rKF
r
K
rKFrkV SS
)12(cosh1''
2sinh1'')(21
KKF
r
K
rKF
r
K
rKFrnrrV TSS
2
21 ''2)12(cosh1
'3'2sinh1
''3)(ˆˆ
VSO2 & VSO3 =0
when m1=m2
![Page 6: Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of Physics, Inha University.](https://reader035.fdocuments.us/reader035/viewer/2022062806/56649f435503460f94c63f29/html5/thumbnails/6.jpg)
Inha Nuclear Physics Group
2-Body Constraint Dynamics
HereF=(L-3G)/2 and K=(G+L)/2 G(A)=-(1/2) ln(1-2A/w) L=(1/2) ln[(1+2(S-A)/w+S2/m2)/(1-2A/w)] w : center of mass energy
l’(r)= -(1/2r)(E2M2-E1M1)/(E2M1+E1M2)(L-G)’
q’(r)=(1/2r) )(E1M2-E2M1)/(E2M1+E1M2)(L-G)’
m(r)=-(1/2)∇2G+(3/4)G’2+G’F’-K’2
k(r)=(1/2)∇2G-(1/2)G’2-G’F’-(1/2)(G’/r)+(K’/r)n(r)=∇2K-(1/2)∇2G-2K’F’+G’F’+(3G’/2r)-(3K’/r)
![Page 7: Inha Nuclear Physics Group Relativistic Approach to QQ Potential 2007. 12. 14 Jin-Hee Yoon Dept. of Physics, Inha University.](https://reader035.fdocuments.us/reader035/viewer/2022062806/56649f435503460f94c63f29/html5/thumbnails/7.jpg)
Inha Nuclear Physics Group
2-Body Constraint Dynamics
VSO2=0 and VSO3=0 when m1=m2
For singlet state, no spin-orbit contribution ←VD+VTSO+VSS+VTSS=0
H=p2+2mwS+S2+2wA-A2
0221 SLL
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Inha Nuclear Physics Group
Relativistic Application(1)
Applied to the Binding Energy of chamoniumWithout spin-spin interaction M(exp)=3.067 GeV Compare the result with PRC 65, 034902 (2002)
T/Tc BE(non-rel.) BE(rel.) Rel. Error(%)0 -0.67 -0.61 9.00.6 -0.56 -0.52 7.10.7 -0.44 -0.41 6.80.8 -0.31 -0.30 3.20.9 -0.18 -0.17 4.01.0 -0.0076 -0.0076
0.0 At zero temperature, 10% difference at most!
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Inha Nuclear Physics Group
Relativistic Application(2)
With spin-spin interaction M(S=0) = 3.09693 GeV
M(S=1) = 2.9788 GeV At T=0, relativistic treatment gives
BE(S=0) = -0.682 GeVBE(S=1) = -0.586 GeV
Spin-spin splitting ∼100 MeV
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Inha Nuclear Physics Group
Overview of QQ Potential(1)
Pure Coulomb :
BE=-0.0148 GeV for color-singlet=-0.0129 GeV for color-triplet(no convergence)
+ Log factor :
BE=-0.0124 GeV for color-singlet=-0.0122 GeV for color-triplet
+ Screening :
BE=-0.0124 GeV for color-singletNo bound state for color-triplet
0 and 2.0
Sr
A
0 and 1
ln21
2.0
22
2
S
rer
A
0 and 1
ln21
2.0
22
2
S
rer
eA
r
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Inha Nuclear Physics Group
Overview of QQ Potential(2)
+ String tension(with no spin-spin interaction)
When b=0.17 BE=-0.3547 GeVWhen b=0.2 BE=-0.5257 GeVToo much sensitive to parameters!
brS
rer
eA
r
and 1
ln21
2.0
22
2
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Inha Nuclear Physics Group
QQ PotentialModified Richardson Potential
27
12
32
11
4
f
s
n
22
2
1ln
213
4
rer
eA
r
s
rS 2
27
8
and
Parameters : And mass=m(T)
A : color-Coulomb interaction with the screeningS : linear interaction for confinement
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Inha Nuclear Physics Group
V(J/)
Too Much Attractive!
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Inha Nuclear Physics Group
V(J/) *r2
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Inha Nuclear Physics Group
V(J/) *r3
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Inha Nuclear Physics Group
Vso(J/)
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Inha Nuclear Physics Group
V(J/)*r2.5
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Inha Nuclear Physics Group
V(J/) at small range
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Inha Nuclear Physics Group
V(J/) with mixing
For J/, S=1 and J=1.
Without mixing(L=0 only), splitting is reversed.
Therefore there has to be mixing between L=0 and L=2 states.
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Inha Nuclear Physics Group
V(J/) with mixing
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Inha Nuclear Physics Group
Work on process
To solve the S-eq. numerically,We introduce basis functionsn(r)=Nnrlexp(-n2r2/2) Ylm
n(r)=Nnrlexp(-r/n) Ylm
n(r)=Nnrlexp(-r/√n) Ylm
… None of the above is orthogonal. We can calculate <p2> analytically, but all the other terms has t
o be done numerically. The solution is used as an input again → need an iteration Basis ftns. depend on the choice of quite sensitively and there
fore on the choice of the range of r.
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Inha Nuclear Physics Group
Future Work
Find the QQ potential which describes the mass spectrum of mesons and quarkonia well.Extends this potential to non-zero temperature.Find the dissociation temperature and cross section of a heavy quarkonium.And more…
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Inha Nuclear Physics Group
Thank YouFor your attention.